Question

Determinati numerele rationale a şi b astfel încât..... va rog mult!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!​

Answer 1

Răspuns:

Rationalizam numitorul la fractia din stanga prin inmultirea ei cu rad5+1

(a+brad5)(rad5+1)/1 = 1+2b

arad5+a+5b+brad5=1+2b

(a+5b)+(a+b)rad5=1+2b

Deci

a+5b=1+2b

a+b=0

-b+5b=1+2b

b=1/2

a= - 1/2

Answer 2

$\it \dfrac{a+b\sqrt5}{\sqrt5-2}=1+2b \Rightarrow a+b\sqrt5=(\sqrt5-2)(1+2b) \Rightarrow \\ \\ \\ \Rightarrow a+b\sqrt5=\sqrt5+2b\sqrt5 -2-4b \Rightarrow a+2+4b=\sqrt5+2b\sqrt5-b\sqrt5 \Rightarrow \\ \\ \\ \Rightarrow a+2+4b=\sqrt5+b\sqrt5 \Rightarrow a+2+4b=\sqrt5(1+b) \Rightarrow \begin{cases} \it 1+b=0 \Rightarrow b=-1\\ \\ \it a+2+4b=0 \Rightarrow a=2\end{cases}$